I have only slow modem connection at home. Can I download sources somewhere else and add them to my system?

Definitely. You can run emerge --pretend package to see what programs are going to be installed. To find out the sources for those packages and where to download the sources from, you can run emerge -fp package. Download sources and bring them on any media home. Put the sources into /usr/portage/distfiles/ and then simply run emerge package. Be warned, however, that this is a tedious process.